When producing a three-dimensional object by rapid prototyping a solidifiable substance is applied layerwise onto a support or onto a previous layer, respectively, and solidified for each layer using radiation, for example a focused light beam, at those places of the layer which correspond to the cross-section of the object. If the applied material is a powder and solidified using laser beams, the method is called laser sintering. Such a method is for example known from U.S. Pat. No. 4,863,538. If a liquid photocurable material is used, the method is called stereolithography. Such a method is for example known from U.S. Pat. No. 5,014,207.
The applicant is aware that for the laser sintering the laser beam may be passed over the layer to be solidified according to a line pattern, for example in meanders as shown in FIG. 1.
FIG. 1 shows a top view of a layer to be solidified 1 of a three-dimensional object to be formed in a coordinate system having a x-direction and a y-direction. In this method a line pattern 2 is determined which depends on the geometry of the layer. The line pattern 2 comprises parallel lines spaced from each other by a distance d. For solidifying the layer I the laser beam is passed with a constant speed v across the surface of the layer 1 to be solidified along the line pattern 2 in the direction indicated by the arrow. Owing to the irregular cross-section of the object in this layer the lines have different lengths L.
FIG. 2 shows the density of the layer to be solidified as a function of the layer geometry, i.e. indirectly as a function of the length of the lines passed by the laser beam. It turns out that the density of the layer to be solidified decreases with increasing length of the lines. In summary, this method produces an inhomogeneous density distribution in the layer to be solidified if the line pattern which is followed by the beam for solidifying the layer comprises lines having different lengths and if the beam passes over the layer with a constant speed.
The occurance of the inhomogeneous density distribution as a function of the line length of the line pattern 2, as shown in FIG. 2, can be explained as follows: Generally, rally, the spacing d of the lines of the line pattern is twice or four times smaller than the diameter of the laser beam cross-section on the surface of the layer 1 to be solidified. Thus, a section on a line can be scanned up to five times if the cross-section of the beam is passed along adjacent lines. With a smaller line length a portion of this line is therefore scanned in rapid succession. It is therefore possible to keep this section nearly continuously on a temperature which is higher than or equal to the sintering temperature. Losses by heat conduction are compensated by the rapid timely sequence of the scans. Thus, the input of energy which directly contributes to the sintering process is high in this section and the material to be sintered has a high portion of liquid phase. A high density is produced during the solidification in such a section.
However, if the beam is passed along a long line, a section along this line cools down to ist original temperature owing to heat conduction losses after the passage of the beam cross section over this section. When again scanning this section it must again be heated up to the sintering temperature. Thus, losses due to heat conduction and reheating cannot be compensated in such a section and a solidification occurs with a density which is smaller than the density of the substance in the section having the smaller line length.
Such an inhomogeneous density distribution within the layer to be solidified and therefore within a three-dimensional object to be formed causes, during the scanning operation, internal mechanical stress producing a deformation of the three-dimensional object to be formed and therefore a loss in its manufacturing precision.
It is the object of the present invention to provide a method and an apparatus for producing a three-dimensional object using rapid prototyping, whereby a homogeneous density distribution is guaranteed in a three-dimensional object to be formed even if the object is produced in layers having arbitrary cross-sectional geometries and if the scanning is made using line patterns comprising lines of different lengths.